This trophy should pop upon launching and completing the 32nd level of the main game, "34FREE", which will become available after you are forced out of the game at the end of "32CORE".
There does seem to be a glitch in the Playstation version where the the trophy won't pop on the first play. The simplest solution seems to be to go to SETTINGS and RESET. This will not wipe your progress, and all you need to do is scroll down to the relevant level and play through it.
*Note: It does not require you to watch the credits.